﻿namespace ProblemsSet
{
    public class Problem_28 : BaseProblem
    {
        public override object GetResult()
        {
            return SummDiagsSpiral(1001);
        }

        public static long SummDiagsSpiral(long width)
        {
            var n = (width - 1)/2+1;
            var res = 8*n*(n + 1)*(2*n + 1)/3 - 14*n*(n + 1) + 16*n - 3;
            return res;
        }

        public override string Problem
        {
            get
            {
                return @"Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 669171001;
            }
        }
    }
}
